Circuits Problems

The specific principles required are indicated in italics at
the beginning of each problem.

Ohm's Law: Because of your physics background, you
landed a summer job as an assistant technician for a
telephone company in California. During a recent
earthquake, a 1.0-mile long underground telephone line is
crushed at some point. This telephone line is made up of
two parallel copper wires of the same diameter and same
length, which are normally not connected. At the place
where the line is crushed, the two wires make contact.
Your boss wants you to find this place so that the wire
can be dug up and fixed. You disconnect the line from the
telephone system by disconnecting both wires of the line
at both ends. You then go to one end of the line and
connect one terminal of a 6.0-V battery to one wire, and
the other terminal of the battery to one terminal of an
ammeter (which has essentially zero resistance). When the
other terminal of the ammeter is connected to the other
wire, the ammeter shows that the current through the wire
is 1 A. You then disconnect everything and travel to the
other end of the telephone line, where you repeat the
process and find a current of 1/3 A.

Ohm's Law:You have a summer job in the
University ecology lab. Your supervisor asks you to
duplicate an electromagnet that she has borrowed. She
tells you that this electromagnet is made by wrapping a
wire many times around a piece of iron and provides you
with all the parts, the same type of wire of the same
diameter and an identical iron core. What you need to
know is how much wire to wrap around the iron.
Unfortunately, you cannot simply unwrap the wire from the
borrowed magnet because that will destroy it. On the side
of the electromagnet, it tells you that when a potential
difference of 12 V is put across the ends of its wire,
there is a current of 0.06 A through the wire. With a
brilliant flash of insight, you realize that the
cross-sectional area and the conductivity is the same for
both the magnet's wire and the wire you have, so you can
find the length with a simple experiment. You cut off a
100-foot piece of identical wire from your supply, attach
it to a 1.5-V flashlight battery and measure a current of
0.10 A through that wire. Eureka! you can now find the
length of the magnet's wire.

Electric Power: You and a friend are studying for
an exam and the session goes until the early morning. At
about 4 am you decide to cook some breakfast. Despite
being sleepy you've got the coffee perking. Now you want
to make some waffles but you realize there might be a
problem. The 1000-watt waffle iron and the 600-watt
coffee maker are plugged into the 110 V kitchen
electrical outlets. If you plug in your 700-watt blender,
will you overload the 20 A circuit breaker? The circuit
breaker protects those kitchen circuit wires that have
the most current from carrying too much current. You are
trying to figure out how the electrical outlets are
connected together in a circuit when your friend reminds
you that when you disconnect the coffeepot, the waffle
iron stays on. Now everything is clear.

Electric Power: You and a friend are studying for
a final and the session goes until the early morning.
About 4 AM you decide to cook some breakfast. Despite
being sleepy, things are going well. The waffles are
cooking and the coffee is perking. Should you make some
toast now? The 1000-watt waffle iron and the 600-watt
coffee maker are plugged into kitchen wall electrical
outlets. You will also use a kitchen wall outlet for the
toaster. The kitchen wall outlets are all part of the
same 110-V circuit which has a 20-A circuit breaker (with
negligible resistance) to protect the wire carrying the
largest current from getting too hot. (Some homes have
fuses to do the same job). You know that if you plug in
too many appliances you will overload the circuit
breaker. The toaster label says that its power output is
700 watts.

Electric Power: As a member of the safety group
for the space shuttle scientific program, you have been
asked to evaluate an electronics design change. In order
to improve the reliability of a circuit to be used in the
next shuttle flight, the experimental design team has
suggested adding a second 12 V battery to the circuit.
The equivalent resistances of the proposed design are
shown below. You are worried about the heat generated by
the device with the 20 ohm resistance since it will be
located next to a sensitive low temperature experiment so
you do the appropriate calculation.

Electric Power:
As part of your summer job as a design engineer
at an electronics company, you have been asked to
inspect the circuit shown below. The resistors
are rated at 0.5 Watts, which means they burn-up
if more than 0.5 Watts of power passes through
them. Will the 100W resistor in the circuit
burn-up?

29. Electric Power: While trying to find the power
ratings of your appliances you find their circuit
diagrams. Looking them over, your friend believes there
must be a typo in the circuit diagram of your toaster.
The heating element that toasts the bread is listed as
having a resistance of 5 ohms. A variable resistor, which
is changed by a knob on front of the toaster, has a range
of from 2 to 20 ohms. Your friend feels that an element
with this resistance will not toast bread properly. Based
on the circuit diagram, given below, you decide to
calculate the maximum power output by the heating
element.